In general, when a carrier-modulated signal is received by a receiver, the carrier frequency of the signal is shifted by an unknown amount, due to clock drift at the receiver and/or a Doppler shift due to motion. Further, the known signal may be delayed by an unknown amount of time in the course of traveling from the source to the receiver. The signal that is received at the receiver is generally referred to as the received signal, and it typically includes noise. For many applications, one needs to determine the shift of the carrier frequency to a high degree of accuracy in order to be able to estimate some of the signal parameters such as the signal delay or the data that are being communicated through the signal.
In one approach for estimating the carrier frequency, known as coherent processing, multiple candidate carrier frequencies are examined. For each candidate frequency, In Phase (“I”) and Quadrature (“Q”) correlation sums are calculated, followed by an evaluation of the sum of squares I2+Q2. The candidate frequency that results in the largest sum of squares is selected as the estimated carrier frequency. If the delay is an unknown quantity, then a two-dimensional search is performed to simultaneously estimate the delay and carrier frequency.
A significant disadvantage to the above approach is that the computational expense in performing the calculations for the various candidate frequencies can be prohibitively high. This is because the number of candidate frequencies that have to be examined must increase in proportion to the duration of the signal and therefore in proportion to the number N of available samples of the received signal. Consequently, the overall computational effort is of the order of at least N2.
In another approach, the signal is broken into multiple short blocks, each block is processed coherently as above, and then the values of I2+Q2 calculated from the different blocks are added. This approach, known as non-coherent processing, can work with a smaller number of candidate frequencies, compared to coherent processing. On the other hand, it is much more sensitive to noise. Therefore, in order to maintain a constant level of performance, more signal samples are required and the overall computational effort remains high. Based on the foregoing, there is a clear need for a Technique for synthesizing coherent correlation sums at a fine frequency resolution using coherent correlation sums that are calculated at a coarse frequency resolution that requires less computational expense.